A strain wave gearing wherein the tooth profile of an external teeth of a cup-shaped or silk-hat-shaped external gear is set as follows. The tooth-tip tooth thickness decreases gradually from an external-teeth outer end toward an external-teeth inner end along an external tooth trace direction. In addition, a pressure angle at a pitch point (P) increases gradually from the external-teeth outer end toward the external-teeth inner end along the external tooth trace direction. Thus, it is possible to realize a cup-type or silk-hat-type strain wave gearing in which external teeth mesh with internal teeth in a wide range along the tooth trace direction, rather than only in one cross-section perpendicular to the axis in the tooth trace direction.